During Tuesday's press conference, Cain flatly denied the allegations, hinting that the rumors might have been disseminated by "the Democratic machine." Cain, the former CEO of Godfather's Pizza and president of the National Restaurant Assn., also said he would not pull out of the race, stating that withdrawal "ain't gonna happen."

It's not currently known if the candidate will discuss the harassment allegations during his "Letterman" appearance. Perhaps Cain is hoping that Letterman, who's no stranger to sexual peccadilloes, will provide a sympathetic presence.

Perhaps an omen can be divined from that night's musical guest on "Letterman": the indie-rock outfit Grouplove.

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